Theorem orordi

Description: Distribution of disjunction over disjunction. (Contributed by NM, 25-Feb-1995)

	Ref	Expression
Assertion	orordi	|- ( ( ph \/ ( ps \/ ch ) ) <-> ( ( ph \/ ps ) \/ ( ph \/ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		oridm	|- ( ( ph \/ ph ) <-> ph )
2	1	orbi1i	|- ( ( ( ph \/ ph ) \/ ( ps \/ ch ) ) <-> ( ph \/ ( ps \/ ch ) ) )
3		or4	|- ( ( ( ph \/ ph ) \/ ( ps \/ ch ) ) <-> ( ( ph \/ ps ) \/ ( ph \/ ch ) ) )
4	2 3	bitr3i	|- ( ( ph \/ ( ps \/ ch ) ) <-> ( ( ph \/ ps ) \/ ( ph \/ ch ) ) )